I think I may have spotted your problem. Been there and got the t-shirt myself.
Ignore the "option" component. This is added by Appery and used if you want to hard code options. Put your model info and options on the "select" component instead.
Look at the breadcrumb in your attached image select2.png and you are setting the "ng-" attributes on selectoption4 under options3 under select3.
Change that so that (a) you only have one "option" component on the "select" and (b) the "ng-" entries are on select3 instead and then it will work.